Syllogism

A syllogism is a structured logical argument in which a conclusion is reached as a necessary result of two premises. Aristotle defined a syllogism as, "a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so."

Contents

Basic structure

A properly constructed syllogism consists of a major premise, a minor premise, and a conclusion. The conclusion has a subject (S) and a predicate (P) which are derived from the premises. The major premise addresses the predicate, the minor premise addresses the subject and the two premises share a minor (or middle) term (M) which connects them. For example:

Major premise: All M are P.

Minor premise: All S are M.

Conclusion: All S are P.

Figures

While the subject-predicate order of the conclusion is fixed, the premises can be structured with the middle term as either the subject or the predicate. The ability to swap terms in the premises results in 4 possible syllogistic configurations known as "figures". The following table shows the 4 possible figures:

Figure 1

Figure 2

Figure 3

Figure 4

Major premise:

M–P

P–M

M–P

P–M

Minor premise:

S–M

S–M

M–S

M–S

Conclusion:

S–P

S–P

S–P

S–P

Types

While figures define the structured order of the argument, type defines the logical style or nature of each premise and the conclusion. There are four possible types, each of which has traditionally been associated with a vowel:

Vowel

Type

Example

A

universal affirmative

"all A are B"

I

particular affirmative

"some A are B"

E

universal negative

"no A are B"

O

particular negative

"some A are not B"

The 4 type designations result in 256 possible types of syllogisms, though most of them are invalid. When the type designation is applied to the major premise, the minor premise and the conclusion, in that order, we arrive at a "shorthand" definition of the argument, like AAA or AEO. The figure number can be appended to this designation (IOE-3) to further define the argument.

As the type designators are vowels, this shorthand has been used to form form mnemonic names for each of the valid forms. The following table shows the names associated with valid arguments, by figure: